<PAGE>

DRAFT: 15 MAY 2003

                                                                    EXHIBIT 10.7

                     [ON THE LETTERHEAD OF BARCLAYS CAPITAL]

To:      Toreador Resources Corporation
         4809 Cole Ave.
         Dallas, TX 75205

Attention: Doug Weir

                                                                    19 May, 2003

Dear Sirs

                             WARRANT BUYBACK LETTER

This is the Warrant Buyback Letter, referred to in the waiver letter dated 19th
May, 2003 (the "MAY WAIVER LETTER"), between Toreador and the Facility Agent.

We refer to the credit agreement dated 30th March, 2001 (the "CREDIT AGREEMENT")
and the settlement fee letter dated on or about today's date (the "SETTLEMENT
FEE LETTER"). Capitalised terms defined or used in the Credit Agreement, the May
Waiver Letter and the Settlement Fee Letter have the same meaning in this
letter.

1.       Subject to your agreement to the terms of the Settlement Fee Letter,
         and subject further to the conditions set forth in paragraphs 2 and 3
         below, we agree to sell and deliver to Toreador and Toreador agrees to
         purchase, on the Settlement Date, those Warrants numbered 18-25
         inclusive issued and delivered by Toreador to Barclays Bank PLC
         ("BARCLAYS") pursuant to the Warrant Letters.

2.       As consideration for the sale and delivery of Warrants numbered 18-25
         inclusive by Barclays Capital in accordance with paragraph 1 above,
         Toreador agrees to pay to Barclays on the Settlement Date a sum of
         U.S.$100,000 (the "REPURCHASE AMOUNT") in cash to the account specified
         in paragraph 5 of the Settlement Fee Letter.

3.       The obligations of Barclays Capital pursuant to paragraph 1 above shall
         be expressly conditioned upon the occurrence of the Settlement Date and
         the payment by Toreador of the Repurchase Amount

4.       Barclays Capital shall fulfil its obligations under paragraph 1 above
         promptly after the fulfilment to its satisfaction of the conditions set
         forth in paragraph 3 above.

5.       This letter may be executed in any number of counterparts, each of
         which shall constitute an original and all of which shall collectively
         and separately constitute one and the same agreement.

6.       This letter is governed by and shall be construed in accordance with
         English law.

7.       Please countersign this letter (or a copy of it) where marked below to
         confirm your agreement to its terms.

<PAGE>

8.       If a provision of this letter is or becomes illegal, invalid or
         unenforceable in any jurisdiction, that shall not affect;

         (a)      the legality, validity or enforceability, in that jurisdiction
                  or any other provision of this letter; or

         (b)      the legality, validity or enforceability, in other
                  jurisdictions of that or any other provision of this letter.

Yours faithfully

/s/ STEVEN FUNNELL
----------------------------------------
For and on behalf of
BARCLAYS CAPITAL
(the investment banking division of Barclays Bank PLC)

Accepted and agreed:

/s/ DOUGLAS W. WEIR
----------------------------------------
TOREADOR RESOURCES CORPORATION

Date: May 19, 2003

                                       2